If you can afford it, I don't think it is possible to have too many
versions of the Beethoven Quartets.  I am fascinated by the differences
in the music, based on which quartet is at work.  Sometimes one group won't
satisfy.  On another day, my mood has changed and I prefer a different one.
I haven't heard the Medici, but they have two different recordings, don't
they?

If you must only own one, I would recommend the Tokyo String Quartet, the
Berg Quartet, or the Emerson Quartet...  even though they are so different
from each other...  anyone will be a prize in your collection.

If you are not compulsive about the sound quality, go for the early
Guarneri, the early Juilliard, the Busch, or the Quartetto Italiano...  if
you can find them...  I think each of these is truly special and a treasure
for any good collection.  The Lener is reportedly very good, but I have yet
to locate a copy.  There is a set on Olympic that is fine, but their name
escapes me at the moment.

I don't know of any truly awful recordings.  It takes so much work and
artistry to put an entire set together, that each has a place and a value.

Ray Bayles